Download or read book Mathematical Theory Of Elasticity And Generalized Dynamics Of Quasicrystals And Its Applications written by Tian-you Fan and published by World Scientific. This book was released on 2023-12-27 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description on mathematical theory of elasticity and generalized dynamics of solid quasicrystals and its applications.The Chinese edition of the book Mathematical Theory of Elasticity of Quasicrystals and Its Applications was published by the Beijing Institute of Technology Press in 1999, written by Prof Tian-You Fan. In this English edition of the book, the phonon-phason dynamics, defect dynamics and hydrodynamics of solid quasicrystals are included, so the scope of the book is beyond elasticity. Hence, the title in this edition is changed to Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications. This book is the first and only monograph in the scope of quasicrystals since first published in 1999 in China and worldwide. In this edition, the two-dimensional quasicrystals of second kind, soft-matter quasicrystals and photonic bade-gap and application of photonic quasicrystals are added.This book combines the mechanical and physical behavior of quasicrystals and mathematical physics, which may help graduate students and researchers in the fields of new materials, condensed matter physics, applied mathematics and engineering science.

Download or read book Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications written by Tian-You Fan and published by World Scientific Publishing Company. This book was released on 2023-12-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed description on mathematical theory of elasticity and generalized dynamics of solid quasicrystals and its applications.The Chinese edition of the book Mathematical Theory of Elasticity of Quasicrystals and Its Applications was published by the Beijing Institute of Technology Press in 1999, written by Prof Tian-You Fan. In this English edition of the book, the phonon-phason dynamics, defect dynamics and hydrodynamics of solid quasicrystals are included, so the scope of the book is beyond elasticity. Hence, the title in this edition is changed to Mathematical Theory of Elasticity and Generalized Dynamics of Quasicrystals and Its Applications. This book is the first and only monograph in the scope of quasicrystals since first published in 1999 in China and worldwide. In this edition, the two-dimensional quasicrystals of second kind, soft-matter quasicrystals and photonic bade-gap and application of photonic quasicrystals are added.This book combines the mechanical and physical behavior of quasicrystals and mathematical physics, which may help graduate students and researchers in the fields of new materials, condensed matter physics, applied mathematics and engineering science.

Download or read book Generalized Dynamics of Soft Matter Quasicrystals written by Tian-You Fan and published by Springer. This book was released on 2017-10-14 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

Download or read book Generalized Dynamics of Soft Matter Quasicrystals written by Tian-You Fan and published by Springer Nature. This book was released on 2022-01-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

Download or read book Mathematical Theory of Elasticity of Quasicrystals and Its Applications written by Tianyou Fan and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.

Download or read book Mathematical Theory of Elasticity of Quasicrystals and Its Applications written by Tian-You Fan and published by Springer. This book was released on 2016-09-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.

Download or read book Fracture Mechanics Applications written by Hayri Baytan Ozmen and published by BoD – Books on Demand. This book was released on 2020-09-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fracture mechanics deals with the cracking behavior of materials, and cracking defines the limit state for many components of engineering systems. Fracture mechanics principles can help us design more robust components to ensure safer airplanes, space shuttles, ships, cranes, buildings, bridges, and mechanical systems. Written by researchers and experts of the field, this book examines recent progress in fracture mechanics applications. Chapters cover such topics as rupture theory, the J-integral, knitted fabric-reinforced polymer composites, and artificial neural networks to detect structural damage, among others. This volume is designed for graduate students, researchers, and practicing engineers.

Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Non Classical Continuum Mechanics written by Gérard A. Maugin and published by Springer. This book was released on 2016-09-24 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

Download or read book Generalized Dynamics of Soft Matter Quasicrystals written by Tian-You Fan and published by . This book was released on 2017 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Integral Equations Boundary Value Problems and Related Problems written by Xing Li and published by World Scientific. This book was released on 2013 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.

Download or read book Mathematical Theory of Elastic Structures written by Kang Feng and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasticity theory is a classical discipline. The mathematical theory of elasticity in mechanics, especially the linearized theory, is quite mature, and is one of the foundations of several engineering sciences. In the last twenty years, there has been significant progress in several areas closely related to this classical field, this applies in particular to the following two areas. First, progress has been made in numerical methods, especially the development of the finite element method. The finite element method, which was independently created and developed in different ways by sci entists both in China and in the West, is a kind of systematic and modern numerical method for solving partial differential equations, especially el liptic equations. Experience has shown that the finite element method is efficient enough to solve problems in an extremely wide range of applica tions of elastic mechanics. In particular, the finite element method is very suitable for highly complicated problems. One of the authors (Feng) of this book had the good fortune to participate in the work of creating and establishing the theoretical basis of the finite element method. He thought in the early sixties that the method could be used to solve computational problems of solid mechanics by computers. Later practice justified and still continues to justify this point of view. The authors believe that it is now time to include the finite element method as an important part of the content of a textbook of modern elastic mechanics.

Download or read book Introduction to the Mathematics of Quasicrystals written by Marko V. Jaric and published by Elsevier. This book was released on 2012-12-02 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Mathematics of Quasicrystals provides a pedagogical introduction to mathematical concepts and results necessary for a quantitative description or analysis of quasicrystals. This book is organized into five chapters that cover the three mathematical areas most relevant to quasicrystals, namely, the theory of almost periodic functions, the theory of aperiodic tilings, and group theory. Chapter 1 describes the aspects of the theory of tiling in two- and three-dimensional space that are important for understanding some of the ways in which "classical mathematical crystallography is being generalized; this process is to include possible models for aperiodic crystals. Chapter 2 examines the non-local nature of assembly "mistakes that might have significance to the quasicrystals growth. This chapter also describes how closely a physical quasicrystal might be able to approximate a three-dimensional version of tilings. Chapter 3 discusses the theoretical background and concepts of group theory of icosahedral quasicrystals. Chapter 4 presents the local properties of the three-dimensional Penrose tilings and their global construction is described through the projection method. This chapter emphasizes the relationship between quasiperiodic sets of points and quasiperiodic tiling. Chapter 5 explores the analysis of defects in quasicrystals and their kinetics, as well as some properties of the perfect system. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.

Download or read book Fractals Quasicrystals Chaos Knots and Algebraic Quantum Mechanics written by Anton Amann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the workshop on "New Theoretical Concepts in Physical Chemistry", one of the participants made an attempt to present a first impression of its achievements from his own personal standpoint. Appar ently his views reflected a general feeling, so that the organizers thought they would be suitable as a presentation of the proceedings for future readers. That is the background from which this foreword was born. The scope of the workshop is a very broad one. There are contribu tions from mathematics, physics, crystallography, chemistry and biology; the problems are approached either by means of axiomatic and rigorous methods, or at an empirical phenomenological level. This same diversifi cation can be found in the new basic concepts presented. Some arise from pure theoretical investigation in C*-algebra or in quantum probability theory; others from an analysis of very complex experimental data like nuclear energy levels, or processes on the frontier between classical and quantum physics; others again have their origin in the discovery of new ordered structures like the icosahedral crystal phases, or the knots of DNA molecules; others follow from the application of ideas like frac tals or chaos to new fields like spectral theory or chemical reactions. It is to be expected that readers will have to face the same sort of difficulties as did the participants in understanding such diverse languages, in applying themselves to subjects possibly far from their own experience, and in grasping highly sophisticated new concepts.

Download or read book Directions in Mathematical Quasicrystals written by Michael Baake and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes twelve solicited articles which survey the current state of knowledge and some of the open questions on the mathematics of aperiodic order. A number of the articles deal with the sophisticated mathematical ideas that are being developed from physical motivations. Many prominent mathematical aspects of the subject are presented, including the geometry of aperiodic point sets and their diffractive properties, self-affine tilings, the role of $C*$-algebras in tiling theory, and the interconnections between symmetry and aperiodic point sets. Also discussed are the question of pure point diffraction of general model sets, the arithmetic of shelling icosahedral quasicrystals, and the study of self-similar measures on model sets. From the physical perspective, articles reflect approaches to the mathematics of quasicrystal growth and the Wulff shape, recent results on the spectral nature of aperiodic Schrödinger operators with implications to transport theory, the characterization of spectra through gap-labelling, and the mathematics of planar dimer models. A selective bibliography with comments is also provided to assist the reader in getting an overview of the field. The book will serve as a comprehensive guide and an inspiration to those interested in learning more about this intriguing subject.

Download or read book Treatise on Classical Elasticity written by Petre P. Teodorescu and published by Springer. This book was released on 2013-05-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.

Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second book of a three-volume set, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. Theory of Plates also illustrates how asymptotic methods allow for justification of the Kirchhoff–Love theory of nonlinear elastic plates and presents a detailed mathematical analysis of the von Kármán equations. An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.